Allstat members' replies (summarized below) appear to confirm my belief
that "margin of error" is distinct from "confidence interval" but is
widely used as a synonym, especially in non-technical writing.  I
particularly liked Stephen Hope's clarification that a survey may be
commissioned with a pre-set confidence interval (CI), and that would
correspond to my use of margin of error (ME) as a specification. The ME is
then used to determine the sample size, so results can be reported with a
known CI. The actual CI may, however, be smaller than the ME and should be
reported as such.  Use by journalists as a shorthand for CI with the
associated p-value omitted invites the lay reader to assume that it is a
100% CI - once a hypothesis has been accepted, the possibility of Type 1
error is ignored.

Allan

-------------------------------------------------------
Date: Tue, 3 Jun 2003 12:07:38 +0100
From: R. Allan Reese <[log in to unmask]>
Subject: Margin of error

A student has submitted work using the phrase "margin of error".  From
checking a few web pages, this appears widely used as a synonym for
confidence interval.  Am I alone in finding this a sloppy misuse?

I would associate "margin of error" with engineering, not as a
probabilistic measure but as the envelope of acceptable range.  As such,
the margin of error is something you specify rather than measure -
inverting the use implies abdicating control.

Comments please, to me.  Should I correct the student, or update my own
thinking?

R. Allan Reese                       Email: [log in to unmask]

-----
From: P. E. Jupp <[log in to unmask]>

>confidence interval.  Am I alone in finding this a sloppy misuse?
        No.
>Comments please, to me.  Should I correct the student, or update my own
>thinking?
        The former.

        Peter Jupp

-----
Date: Tue, 3 Jun 2003 12:25:19 +0100
From: Steven Hope <[log in to unmask]>

In my experience the confidence interval is often a thing that is
specified and studies are designed around it. You get a brief from a
client that says "we'd like the data to be accurate to within +/-5% at
the 95% confidence limits". That seems to me to fit exactly with your
definition of a margin of error - the range of acceptable accuracy, in
this case for survey data.

I guess where you have no control over the design of the study you would
collect your data and measure the confidence interval for the results
but where you are designing the study, the confidence interval is, in
many cases, the key design variable. Where you specify a margin or
error, it implies that you are taking control rather than abdicating it.
Even in engineering or production error tolerances are used to control
processes rather than simply monitor them.

I think what your student means is OK but you are more precise in your
language. He should be too. I think a "confidence interval" has a more
specific meaning than a "margin of error".

Steven Hope
Group Director
NFO Social Research
19 Atholl Crescent
Edinburgh, EH3 8HQ

-----
From: "Southworth, Harry" <[log in to unmask]>

I've come across it as meaning half the width of a confidence interval. It
is used in determining sample size when the aim is to produce a point
estimate and confidence interval, rather than when the aim is to test a
hypothesis.

Harry Southworth,
TW2T/5 Parklands,
Alderley Park,
Cheshire, SK10 4TG, UK

-----
From: Tim Downie <[log in to unmask]>

My opinion is that 'margin of error' is a phrase which the layman
can "understand".  The implication is that the quoted value +/- the
margin of error gives the limits of a confidence interval, which may or
may not be 95% confidence :-).  But this ambiguity is why statisticians
try to keep clear of the phrase, unless writing for a very general
audience (eg. a newspaper report).

As it sounds like the student is doing a statistical or data analytic
project, you should tell him/her to use appropriate formal language.
They can always use the phrase 'margin of error' when describing what a
CI is if the project is aimed at a statistically naive reader.

Dr Tim Downie
Dept. Statistical Science
University College London
Gower Street, London WC1E 6BT

-----
From: Ronan Conroy <[log in to unmask]>

Margin of error is the confidence interval for an individual measurement.
Confidence interval tends to be used for summary statistics.

Or so I thought from misunderstandings with my 'hard science' colleagues.

Ronan M Conroy ([log in to unmask])
Lecturer in Biostatistics
Royal College of Surgeons
Dublin 2, Ireland

-----
From: Emil M Friedman <[log in to unmask]>

In what context was it used?  If the student is trying to communicate with
non-statisticians, his audience may well understand the phrase margin of
error better than the phrase confidence interval.

One could argue that the phrase confidence interval is more rigorously
defined than the phrase margin of error.  On the other hand, most real
situations partially violate the assumptions behind most statistical tests,
so I'm not convinced that rigor is particularly important.

-----
Plus comments received
From: Cor Stolk <[log in to unmask]>
From: Matz David <[log in to unmask]>


Thanks to all who replied,
Allan